Instability and blow-up of solutions of the fifth-order KP equation

Abstract

In this paper, we study the dynamical behavior of solutions of the fifth-order Kadomtsev–Petviashvili equation. We improve the results of the previous works and show strong instability of solitary waves when the coefficient of the third-order dispersion term is positive. In spite of the lack of scaling, by using the variational characteristics of the solitary waves we obtain sharp thresholds for blow-up and global existence by means of new estimates.